A minimum mean-squared error (MSE) beamforming algorithm employing the optimum frac- tional Fourier transform (Opt-FrFT) domain second-order cyclostationarity is proposed. This method can efficiently filter out the compact desired chirp signal, with a consequence that the cyclically un- correlated interferences and stationary (colored) Gaussian noise are greatly suppressed in the Opt- FrFT domain. This improves the MSE minimization cyclic beamformer by reducing effectively the Opt-FrFr domain signal-noise cross terms in the presence of finite data length de-correlation opera- tion. Simulation results show that the new method works well under a wide range of signal-to-noise ratio (SNR) and signal-to-interference ratio (SIR).